WOONSOCKET — The city’s Adopt-A-Family program may be forced to turn away needy families if more donors don’t come forward in time for Christmas, the organization says.

With the sign-up deadline passed, the organization has matched 720 young families with donors, but that leaves 250 more without patrons.

Now Adopt-A-Family is extending its donor registration period by another week in hopes that it will find enough donors to help every needy family this season.

This story is not a new one for the program, now in its 24th year. As demand has grown, Adopt-A-Family has found itself scrambling to find contributors for every eligible family. Each holiday season, that challenge grows more difficult, as gas and rent bills skyrocket.

This year, however, the demand has reached a new high, said Sandra Soares, program coordinator. If more donors don’t step up, a total of about 500 enrolled children could be left without help.

Many of those still in need are working families, who make too much money to qualify for federal and state subsidies and other charitable funds, but don’t have enough stored away to make Christmas special. Those are the families Soares says she worries most about, because they’re less likely to receive help from other sources.

Nearly all the gift recipients are from Woonsocket, but Soares encourages donors from anywhere. In recent years, the program has seen patrons from places such as North Kingstown and East Greenwich, as well as neighboring communities such as Cumberland and Lincoln.

“We have donors from everywhere. Some people move away out of state and still they call us every year to adopt,” Soares said. “They’re looking for something they can do that involves more than just writing a check.”

But for every new donor, there are others who can no longer participate.

“There are a lot of people who aren’t able to adopt-a-family every single year, so we have to find a certain number of donors every year,” she said. That’s the hard part.

Adopt-A-Family donors are asked to provide three to four children’s clothing items as well as two to three toys, Soares says. The program will provide a wish list of a child’s wants and needs and contributors are asked to return the wrapped purchases to the program’s Woonsocket headquarters by the week of Dec. 10. The process is anonymous on both sides.

For more information, or to become a donor, contact Adopt-A-Family at (401) 766-2291.